Correct Answer – Option 1 : \(\frac{{19}}{{18}}\)

Concept:

When a source is moving towards a stationary observer, observed frequency is given by

\({f_{observed}} = f\left( {\frac{v}{{v + {v_s}}}} \right)\)

Where, f = frequency of sound from the source,

v = speed of sound and

v_s = speed of source.

Calculation:

Given,

Speed of the train = 34 m/s

Frequency when the whistle blows is f₁

Speed of the train is reduced to 17 m/s after sometime

Speed of the sound = 340 m/s

Frequency registered after = f₂

Now applying above formula to two different conditions given in problem, we get

f₁ = Observed frequency initially

\(\Rightarrow {f_1} = f\left( {\frac{{340}}{{340 – 34}}} \right)\)

\(\therefore {f_1} = f\left( {\frac{{340}}{{306}}} \right)\)

f₂ = Observed frequency when speed of source is reduced 

\(\Rightarrow {f_2} = f\left( {\frac{{340}}{{340 – 17}}} \right)\)

\(\therefore {f_2} = f\left( {\frac{{340}}{{323}}} \right)\)

So, the ratio f₁ : f₂ is

\(\Rightarrow \frac{{{f_1}}}{{{f_2}}} = \frac{{f\left( {\frac{{340}}{{306}}} \right)}}{{f\left( {\frac{{340}}{{323}}} \right)}} = \frac{{340}}{{306}} \times \frac{{323}}{{340}}\)

\(\Rightarrow \frac{{{f_1}}}{{{f_2}}} = \frac{{323}}{{306}} = \frac{{19}}{{18}}\)

\(\therefore \frac{{{f_1}}}{{{f_2}}} = \frac{{19}}{{18}}\)

Therefore, then the ratio \(\frac{{{f_1}}}{{{f_2}}}{\rm{\;is\;given\;by}}\:\frac{{19}}{{18}}\).

Correct Answer – Option 4 : 152 million km

The correct answer is 152 million km.

• It is approximately the average distance between the Earth and the Sun about 150 million km.
• The Earth-Sun orbit distance is defined to be exactly 1.00, and we call this distance 1.00 AUs.
• An Astronomical unit is a unit of length it is used to measure distances within the Solar System.
• 1 A.U. represents the mean distance between the Earth and our sun.
• The mean distance between the sun and the earth is 149,598,000 km.
• In terms of light-years, it is 8.311 minutes.
  A light-year is a measure of distance and not of time.
• Light travels at a speed of 300,000 km/second.
• It is the distances that light will travel in one year that is taken to be one light year.
• This equals to 9.461×1012 km. 

Correct Answer – Option 3 : 6 × 10^-13 A

The resistance of the mica between the two faces is

\(\rho \frac{l}{A} = \frac{{\left( {1 \times {{10}^{13}}} \right) \times {{10}^{ – 3}}}}{{10.0 \times {{10}^{ – 4}}}}\) 

= 1 × 10¹³ Ω.

The leakage current \(= \frac{{6\;V}}{{1 \times {{10}^{13}}\;{\rm{\Omega }}}} = 6 \times {10^{ – 13}}A\)

Correct Answer – Option 2 : In an elliptical orbit

Concept:

According to the given condition in the question, after collision the mass of combined system is doubled. Also, this system would be displaced from its circular orbit.

So, the combined system revolves around centre of mass of system + earth’ under action of a central force.

Hence, orbit must be elliptical.